Optimal Lot-Sizing/Preventive Replacement Policy for an EMQ Model with Minimal Repairs

Abstract

ABSTRACT A general lost-sales Economic Manufacturing Quality (EMQ) model with machine breakdowns, minimal repairs and planned replacements is considered. When the machine fails, minimal repair is performed in negligible time and production is resumed immediately. It is assumed that resumption cost is lower than the set-up cost incurred at the beginning of each production cycle. Other cost components include inventory holding cost, operating cost, lost-sales cost and the preventive replacement (overhaul) cost. Both time to failure and the time to perform an overhaul are assumed to be generally distributed random variables. The objective is to find the optimal lot-sizing/ preventive replacement policy minimising the long-run expected average cost per unit time. The problem is formulated in the framework of semi-Markov decision processes. It is shown that the optimal lot size is a function of the operating age of the machine and the optimal preventive replacement is an age replacement. An EMQ model with lost sales is studied under the assumption of a constant production lot size. It is shown that a good approximation to the optimal policy can be found by solving two nonlinear equations.